Modelling value-at-risk under normal and extreme market conditions

Troels Thostrup Andersen & Thomas Chr. Frederiksen

Student thesis: Master thesis

Abstract

The thesis nds evidence supporting that the Basel II benchmark model provides poor estimates of the market risk VaR - both over a 10 days, as well as a one day horizon. This is particularly due to the homoskedastic estimates provided by this model, but also because the model assumes returns to be Gaussian and thereby independently and identically distributed. Evidence further suggests that it is na ve to assume that one model su ciently describes the risk in a market which at times seems fairly stable, while at others becomes quite volatile. Analysis of the historical returns show that when divided into a normal and an extreme market, the empirical distribution of both return series has higher kurtosis than assumed by the Gaussian distribution. However, only the extreme market seems negatively skewed. Because of this asymmetry, each side of the distribution of the extreme market should be estimated individually. For this reason and because of other di erences in market characteristics, two individual models are proposed. For the normal market a GARCH(1,1) model is proposed. The advantage of such a model is its ability to incorporate historical error terms in order to deliver heteroskedastic volatility estimates. Because of the prevailing autocorrelation, such a model seems particularly e cient. In order to give accurate VaR estimate in an extreme market setting, a conditional peaks-over-threshold model building on extreme value theory is proposed. This model combines standard POT modelling with GARCH modelling in order to deliver heteroskedastic volatility estimates. The advantage of applying such a model is its ability to give accurate estimates of the individual tails, and thereby conditional volatility estimates, when observations are unevenly distributed.

EducationsMSc in Mathematics , (Graduate Programme) Final Thesis
LanguageEnglish
Publication date2010
Number of pages101